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IEEE Journal of Quantum Electronics

Transient phase conjugation in Kerr media, photorefractive media, and plasmas: a comparison

George C. Papen, J. A. Tataronis, Bahaa E. A. Saleh

Published Mar 1, 1989• 5 citations
Publisher

Abstract

A general solution to a linearized transient problem is presented and is shown to be valid for Kerr materials, photorefractive materials, and plasmas. The solution is expressed in terms of a transfer function that relates the complex frequencies of the probe and the conjugate field. Using this solution, the parameters that govern the overall time behavior are identified and compared. These parameters are then used to discuss the distortion characteristics of the conjugate signal for each of the three materials.>

DOI
10.1109/3.18567

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Physical Review A•May 1, 1995•10 citations
A general solution to a linearized transient problem is presented and is shown to be valid for Kerr materials, photorefractive materials, and plasmas. The solution is expressed in terms of a transfer function that relates the complex frequencies of the probe and the conjugate field. Using this solution, the parameters that govern the overall time behavior are identified and compared. These parameters are then used to discuss the distortion characteristics of the conjugate signal for each of the three materials.>
We explore dynamic media, such as plasmas and photorefractive materials, as generators of phase conjugated replicas of transient optical signals via four-wave mixing. The characterizing element of dynamic media is a population of free charge carriers that leads to induced charge density gratings on probe illumination. In steady-state conditions, phase conjugation in such media normally appears with smaller pump intensities than are required in Kerr media but at the expense of potentially slow response times.1
Using perturbation theory, we examine the fidelity of the photorefractive degenerate four-wave mixing (DFWM) phase conju- gator when the probe wave is spatially and temporally varying. Previous theories are based on linearized undepleted pump approximation and Laplace transform technique. Fully nonlinear solutions assume a single monochromatic plane wave probe. We have considered instead the more general case in which the probe is spatially varying (a beam) and/or temporally varying (a pulse), and the pumps are allowed to deplete. The probe wave is expanded as a sum of monochromatic plane waves of frequencies ω j = ω p + Ω j , wavevectors k j , and complex amplitudes A j (Ω j , k j ), where ω p is the frequency of the pumps. Using a perturbation approach up to the third order, we found that the components of the probe interact in pairs, so that the component of the conjugate wave at −Ω l −k l is H(Ω l , k l ) is the linearized response, ρ(Ω l , k l ; Ω j , k j ) represents crosstalk when j ≠ l, and self-nonlinear effect otherwise. Both functions exhibit resonance behavior. We use Eq. (1) to determine the response of the conjugate to pulsed beams.
We demonstrate for the first time, to our knowledge, second harmonic optical phase conjugation, using the second spatial harmonics of a nonsinusoidal grating formed in a photorefractive material. The possibility of harmonic phase conjugation has been considered previously for artificial Kerr media.1 We have applied the same idea to barium titanate, since the existence of the higher-order gratings in this material has been known to us for some time. In our experiment, two 1.06-µm cw Nd:YAG laser beams wrote a grating in a poled photorefractive barium titanate crystal. Then a second harmonic of the YAG at 0.532 µm read out the grating in a counterpropagating direction to one of the writing beams. In this geometry, the usual Bragg condition is not satisfied. The reflectivity of the 0.532-µm signal was rather weak, ~0.01%, with ~0.1-mW reading beam power. The buildup time was around 3 s, with loosely focused writing beams with 50-mW power in each beam. The same experiment with a SBN crystal showed no significant harmonic phase conjugation. Finally, we stress that this effect is different from the previously published result.2
Optical phase conjugation by four-wave mixing in a Kerr medium is considered. Two strong counterpropagating lasers pump a nonlinear medium in which they excite the third-order polarization. Mixing with a weak incident field then generates the phase-conjugated image of that field. It is shown how the polarization of the pumps and the tensorial nature of the nonlinear interaction can be accounted for by a geometrical polarization tensor. The electric field is shown to obey two coupled wave equations, which couple a positive- and negative-frequency component of the field. These wave equations allow plane-wave solutions, and we derive the dispersion relation for the wave vectors of these modes. By matching the field of such a mode across the boundaries of the medium to an external incident field, we are able to obtain analytically the Fresnel coefficients for reflection and transmission. Our expressions reduce to earlier results in the appropriate limits.